Slide rule



2 Sheets-Sheet l INvEN'roR R. B. POOLE SLIDE RULE Filed Nov. 28, 19156 Q@or 5. Poo/ E @ary BY 5:

5 blubb! Dec. 6, 1938.

AT1-ORN EYs 2 Sheets-Sheet 2 R. B. POOLE SLIDE RULE Filed Nov. 28, 1936im N l Y w Dec. 6, 1938.

ATTORN evs L m E INVENTQR /Eov B POOLE Patented Dee e, 1938 2,138,879

UNITED STATES PATENT OFFICE sum-i RULE Roy B. Poole, Dayton, h10Appucetion November 2s, 193s, sensi No. 113,238 s claims. (ci. zas-vo)(Granted under the act or Maren 3, issa, as amended Apni 3o, 192s;` 31oo. G. '151) The invention described herein may be manufurnished on theinwardly disposed edges of the factured and used by or for the Govermentfor bars H and J. Thus the sliding bar I is firmly governmentalpurposes, without the payment to secured against lateral movement and atthe same me of any royalty thereon. time is freely longitudinallyslidable with respect 5 My invention relates to slide rules and more tothe iixed bars H and J. An indicator X, with 5 particularly to a log logduplex slide rule, and the full transparent surfaces overlaying the rulenovelty thereof consists of improvement in the markings of Figs. 1 and 3and a third transparent scales and their arrangement as will be morefully surface overlaying the rule markings of Fig. 2, is hereinafterpointed out. freely slidably mounted upon the aforesaid bars A furtherobject of my invention is to provide a such that it may be readilyadjusted to any prede- 10 slide rule by means of which numerical computatermined position between the plates K. The side tions of an engineeringnature can be solved with transparent surfaces or the indicator X areprogfeel ease, more rapidly, and with greater acvided with the customaryhair lines Y, while the curacy than with any slide rule heretofore inuse. bottom transparent surface of the indicator X is With the foregoingand other objects in view, provided with a hair line Z. 15 which willappear as the description proceeds, the In Fig. 1, the upper portion ofthe bar H is proinvention CODSSS 0f Certain new and novel feavided witha folded logarithmic scale designated tures and combinations, which willbe hereinafter Rl, R2 and Rt, the total length thereof being more fullyillustrated and described in the acthree times that 0f the standard Dscalel The eenlpanyng. drawings and mOle Particularly special purpose ofthis arrangement, as well as 20 pomted out m the appended clamsthe useof certain markings appearing to the Referring 'G0 the drawings, inWhich numerals extreme right thereof, will be discussed in detail O likeCharacter designate Similar parts throughbelow. The next scale on thebar H is the standout the seVealClaimS ard A scale consisting of theusual graduated Fig. 1 shows the front working face of my slidelogarithmic scale of two unit lengths from l to 25 rule. 100,

Fig. 2 shows the bottom edge of Fig. 1 in side For its uppermost scale,the sliding bar I is propfnflle. vided with the standard B scale,graduated the Fig. 3 shows the rear working face of my slide same asscale A on bar H. immediately beneath 30 fille. the B scale ispositioned the standard K scale, Fig. 4 shows an enlarged left-handportion of consisting of three complete logarithmic scales. Fig. 1 withspecial setting of the sliding bar. The third scale on the sliding bar Iis the stand- Fig. 5 shows an enlarged right-hand portion of ard CIwhich is the usual reciprocal logarithmic J Fig. 1. scale of full unitlength, graduated from 10 to 3g Fig. 6 shows an enlarged fragmentgl viewof 1. The fourth and last scale on the sliding bar Fig. 2. I is thestandard C scale, graduated logarith- Fig. l shows an enlargedright-hand portion of mcauy and 0f fun mit length from 1" to 10- Fg, 3The bar J of Fig. 1 is provided with four scales Fig. 8 shows a furtherenlarged end view of the 91S follows: The uppermost, Scad? is thestandard 40 right hand portion of Fig 1. D scale, graduatedlogarithmically, exactly the In Fig. 1, four plates K are iixed to theouter exsame as the C scale on the .sliding bar I' Imtremmes of a bal. Jby means of rivets M. The mediately below the D scale 1s provided afolded bar J is surmounted by a sliding bar I, which in logarithmicscale designated Q2 and QI, the total turn, is surmounted by a bar H.The lasgmamed length being twice that of the standard D scale. 45 bar isveryingiy adjusted, then nxed, with respect The use of Certain markingsappearing to the to the upper ends of the plates K by means of extremeright of the aforesaid scales, and used in screws N. Referring to Fig.8, the slidable bar I conjunction therewith, will be discussed below.has the usual tongue members on each edge there- The fourth and lastscale on the bar J is the standof, adapted to slide in the usual groovemembers ard equal parts L scale. The further use of certain markingsappearing to the extreme left of the four scales referred to above willbe discussed in detail below.

It is now pertinent that reference be made to the new and novelarrangement of certain of the scales" and all of the markings disclosedin Fig. 1. By means of the novel arrangement, the folded scaledesignated RI, R2 and R3; with the indicator X set to any desired numberthereon, the cube of the aforesaid number can be determined directlybelow on the D scale, or conversely; for any setting on the D" scale,the corresponding cube root of the aforesaid number can be read directlyon the folded scale designated RI, R2 and R3. Since the latter isarranged in three folds, a new and novel introduction of markings hasbeen incorporated upon the extreme righthand portion of the bar H, thepurpose of which is to provide an abbreviation of the rules fordetermining the decimal point in the' calculation proposed, whichmarkings further serve to indicate which one of the aforesaid threefolds the result should be read on.

As shown in Fig. 1, the A and B scales occupy their usual position. TheK scale, however, is moved to the sliding bar I and takes the place ofthe standard CIF scale, which is a full length inverted CF scale, foldedon the vertical center line oi the sliding bar I. The foregoingarrangement facilitates the evaluation of such expressions as llaVbXc/l,

etc. It should further be noted that the 0", "CI and D scales occupytheir normal positions.

Through the new and novel interarrangement of the D scale and the foldedQ2 and QI scale,`

the square of any number read on the latter scale is found on the formerscale by means of the indicator X and conversely, the'square root of anynumber on the D scale is obtained directly below on the Q2 and QI scale.Since the latter is arranged in two folds, a new and novel introductionof markings has been incorporated upon the extreme right-hand portion ofthe bar J to indicate, thru appropriate rule abbreviations, which one ofthe aforesaid two folds the result should be read on, and for thefurther purpose of determining the decimal point in the calculationproposed. Following conventional practice, the L scale of equal parts isplaced below the Q2 and QI scale. The common or Briggs logarithm of anynumber on the D scale is read on the L scale by means of the indicator XA further new and novel auxiliary, or offset scale designated C.,covering a range from rightto-left of zero to fifty degrees centigrade,is positioned upon the lowermost left-hand portion of the sliding bar Iand is adapted for alignment with a reference line designated Rpositioned upon the uppermost left-hand portion of the bar J. By meansof the aforesaid scale C. and reference line R, the electricalresistance of copper bar or wire per 1000 foot length can be readilyobtained. in terms of the international standard, for any temperature offrom 0 C. to 50 C., and for any given diameter or area in circular mils.The foregoing is accomplished by bringing the desired temperature on theC. scale into coincidence with the reference line R, then setting theindicator X to the bar or wire diameter required on the Q2 and QI scale.The desired resistance per 1000 feet can then be read on the CI scale.

Determination of the decimal point from the "markings appearing to theright of the Q2 and QI scale has previously been discussed here inabove.

In Fig. 2, the lower portion of the bar J shown in Fig. 1 is providedwith a secondary Q2 and QI scale, the Q2 fold appearing upon the upperportion and the QI fold appearing upon the lower portion of the bar J.In accordance with the Brown and Sharpe system of wire gauges, sizesfrom "1" to 10, are read from extreme right to extreme left on the QI'fold. If the indicator X be set on 1, a corresponding mil reading of 289is obtained on the QI fold of Fig. 1. In like manner, with indicator Xset to "5" or "10 on the QI fold, corresponding mil readings of 182 and"102, respectively, are obtained on the QI fold of Fig. 1. Wire gaugesizes from 11 to 20" are read from extreme right to extreme left on theQ2 f old. The remainlng gauge sizes oi' 21 to 30 and 31" to 40 are foundrespectively upon the QI and Q2 folds. The remaining wire gauges of 0"to 0000" are found upon the left-hand extremity of the Q2' fold. Thespecial significance of certain "markings" appearing to the extremeright of the QI and Q2' scale will be discussed in detail below.-

In Fig. 3, the upper portion of the bar J is provided with a foldedscale designated (left) TI and T2 and (right) CTI and CTZ, the totallength thereof being twice that of the standard trigonometrical T scaleof tangents. Numerical values of. tangents obtainable from the firstfold thereof have a range from 0.1 to 1.0, whereas those obtained fromthe second fold range from 1.0 to 10.0. It should be noted that allfigures referring to co-functions are in red, as are the designationsCTI and CTZ appearing at the extreme right-hand portion of the bar J.The special signiiicance of the 0" and +1 markings appended thereto willbe discussed in detail below. Immediately beneath the above folded scaleis positioned a standard LLO scale giving graduated log-log fractionalor decimal readings from .05 to .97.

The B and "C" scale positioning of the bar I shown in Fig. 1 has beenretained in Fig. 3. Between these scales is interposed a folded scaledesignated (left) SI and S2 and (right) CSI and CS2, the total lengththereof being twice that of the standard trigonometrical S" scale ofsines. The numerical values of sines read upon the first fold thereofrange from 0.01 to 0.10, whereas those read from the second fold rangefrom 0.10 to 1.0. It should be noted that all figures referring toco-functions are in red, as

are the designations "CSI and CS2 appearing at the extreme right-handportion of the bar J. The special significance of the 1 and 0" markingsappended thereto will be discussed in detail below.

The bar H of Fig. 3 is identical in its upper scale arrangement to thatof the bar J of Fig. l. Immediately beneath the D scale is provided afolded scale designated LL3, LL2" and LLI; the first fold thereof beinggraduated through the numerical range from 2.718 to 22,000 or e1 to e1;the second from 1.105 to 2.718 or el/10 to e1; and the third from 1.01to 1.105 or e1/100 to el/IO.

Reference is now made to new and novel arrangements of certain of thescales and all of the markings disclosed in Fig. 3. By interarrangementof the folded TI and T2 scale andl 2,138,879 scale upon the xed upperand cube root of any number from I1" to 10" is the standard D" lowerbars J and H, respectively, and by further interarrangement of thefolded Si and S2 scale and the standard C scale upon common sliding bartangent and co-tangent values can be read directly upon the D scale andsine and cosine values read directly upon the "C scale by means of theindicator X. 'Ihls is thought to be a distinct advancement in the art.

The following examples, showing my new and novel method of accomplishingcertain engineering calculations are given, to more clearly set forththe nature and scope of my improved slide rule. Before proceeding withthe actual examples, and in order to simplify the description of sliderule operations, we will make use of a symbolic notation in which-1z=any given number.

N=the characteristic of any number (n).

Na=the characteristic of any number (a).

Nb=the characteristic of any number (b) etc.

a, b, c, d, e and so on represent numbers used in any numericalcalculation.

Like its logarithmic analogy, the characteristic o! a number, for sliderule purposes, can be defined a follows:

Where N==number of digits in the number (n). Where N=number oi Ospreceding the number (n) for determining the characteristic, or decimalpoint location of any number whose cube is obtained by setting theindicator X to the given number on RI, R2 or R3, and reading the resulton D". Likewise, the group to the right o' this vertical dividing lineis an abbreviation of the rules for determining the characteristic, ordecimal point location of any number whose cube root is obtained, bysetting the indicator X to any given number on D" and reading the resulton Ri, R2 or R3. Considering the left group, it will further be observedthat the notation 3N, 3N-I and 3N-2 lines up respectively with scalesR3, R2 and Ri. The key to this group is placed immediately below andadjacent to the slide I; the notation "CND meaning the cube, orcharacteristic of the cube of any given number read on the D" scale. Thegroup to the right of the dividing line has the notation N, N +1 and N+2lining up respectively with scales R3, R2, and RI; and it is evidentthat, for any characteristic of N, one of these and only one will bedivisible by three as indicated. The relation of (N) /3, (N+l)/3 and(N+2l/3 to the adjoining scales R3, R2 and RI is necessary to thecorrect reading` of a cube root on these scales, as it serves to showclearly which section of the scale the result must be read on, as wellas giving the characteristic of the result. For example, by taking aseries of numbers from 1 to 1000, it is noted that the read on the Riscale, since in this case N=1 and (N4-2) /3=1 as required for thisscale. Likewise, the cube root of any number from 10 to 100 is read onthe R2 scale, for N=2 and (N+1) /3=1 as required; also the cube root ofany number from 100 to 1000 is read on the R3 scale, for N=3 and Nl3=1as required. The key to this group of markings" "CRNR" means the cuberoot, or characteristic of the cube root of any given number read onscale Ri, R2, or R3. Whereas this group of markings is indispensable tothe correct reading of a cube root on the RI, R2 or R3 scale, thereverse is not true; i. e., the correct reading for a cube on the D"scale is always obtained without reference to the markings. The latteris used merely for the purpose of determining the characteristic of theresultant cube as previously explained.

ILLUs'raA'rrvE EXAMPLES Cubes of numbers using scales RI, R2, R3 and "D"Rule I.-If the given number is read on Rl, the characteristic of itscube read on D" is 3 times that of the number less 2; if on R2, it is 3times that of the number less i: and if on R3, it is 3 times that of thenumber.

let a=x Top scale El Intermediate scale R2 Lower scale R3 Nx=5Nal Nx=Na'io find the cube of a number, set the indicator to the given number onRi, R2 or R3, then the coinciding number read on D" is the cube; thecharacteristic being determined by Rule l.

Examples of cubes using scales Ri, R2, R3l and D (Rule 1) 4. Find thevolume and weight of a steel bail 6.5 inches diameter, assuming thatsteel weighs 0.28 lb. per cu. in. Volume V=.5236d3 and weight W=0.28V;hence, place line of indicator to 6.5 on R3 then set .5236 on CI ofslide to indicator. Reading the volume V on scale D un der the leftindex of CI, it is found to be 144 cu. in. Next, move the indicator over0.28 on C and read the Weight W=40Ji lb. on D". By the old method, setindicator to 6.5 on D, set 6.5 on CI" to indicator, set indicator toleft index of"C set 6.5 on CI indicator to left index of C, then set.5236 on CI to indicator when the volume 'V' can be read on D" under theleft index of "C. Resetting the indicator to 0.28 on C gives the weightW on scale D" under the hair line.

Examples of cube roots with scales RI, R2, R3

Rule 2.-Add 0, 1 or 2 to the characteristic of the given number so as tomake it exactly divisible by 3. The quotient after dividing by 3 is thecharacteristic of the cube root. If nothing is added; or, in otherwords, if it is exactly divisible by 3, use scale R3; if 1 is added, useR2; and if 2 is added. use RI.

to indicator., set

v:se

4 :,isaavo Let A1f=x Top scale RI Intermediate scale R2 Lower scale R3N::= Na+2) /3 Nx= Na+1 /3 Nx-.fNa/S 5. (2.125)1/5==1.286 N=(1+2) /3=1UsescaleRl. 6. (40,600)1/3=34.40 N= (5+1) /3=2 Use scale R2. 7.(.00032i)1/3=.0685 N=(3+0) /3=-1 Use scaleRl. n 1 113 R=15=-4,

Q. (605X'7.15)1/3=16.3 R=3+1=4,

N= 4+2 /a=2 Use R" Referring to problems 8 and 9, it will be observedthat the result is obtained without resetting to another scale, as wouldbe necessary with the old arrangement.

Comparing my new arrangement of scales for cubes and cube roots; Ri, R2,R3 and "D with the old arrangement of K and D, it is clear that theformer will give greater accuracy, since the scale lengths are threetimes those ot the latter. Another very decided advantage that can beseen from Example 4 is that when the cube is obtained on the D scale, itcan be multiplied or divided by other factors directly, and thisprocedure cannot be followed with the old arrangement of scales.

Referring to Example 4 it can be observed that with the new scales, thefinal result is obtained with two settings of the indicator and onesetting of the slide; whereas, with the old, four settings of theindicator and three of the slide are required to accomplish an equalresult.

For squares and square roots the scales QI and Q2 are related tothe Dscale, in a manner similar to that used for the cube and cube rootscales. The same advantages are apparent, and a few examples shouldsuiiice to make their use clear.

Squares of numbers using scales QI, Q2 and "D Rule 3.-If the givennumber is read on QI, the characteristic of its square read on D is 213. Find area of circle 41/2 in. diameter. The area A=r/4 D2 hence, setline oi' indicator to 4.5 on Q2, then set special mark representing 1r/4on the CI" scale of slide to indicator and read the area 15.90 sq. in.on D opposite the left index of CI.

Examples of square roots with scales QI, Q2

and D Rule 4.If one added to the characteristic of a number makes itexactly divisible by 2, scale QI should be used, and the characteristicof the root is (N+1)/2; but if the characteristic is exactly divisibleby 2, scale Q2 should be used and 17. Find the diameter of a circlewhose area (A( is 1800 sq. inches. Diameter ...fait

hence. set line of indicator to 1800 on D, then set lett index oi' CI toindicator, next reset indicator to r/4 mark on CI, then the requireddiameter 47.9 inches can be read under the hair line on Q2. With theindicator set to any given number N on scale QI or Q2, the followingpowers and roots can be read from the front working face scales of myimproved slide rule, as shown in Figs. 1 and 5: on D" read N1, on CIread l/N, on K" read N', on A read N4 and on RI, R2 or R3 read Nm. Itwill be observed that expressions such as l/N, N6, and N4 cannot beobtained by direct reading on existing slide rules; furthermore, it isclear that by utilizing al1 the scales shown in Figs. 1 and 5 a largenumber of engineering problems can be solved with less settings andgreater accuracy than with slide rules now in common use. Since it isobviously impossible to give examples of all the combinations possible,the following can be considered representative:

18. Find the moment of inertia of a solid steel shaft 6.5 inches indiameter. T'he moment oi inertia I=.049D4, hence set indicator to 6.5 onQ2, then place the left index of slide in alignment with the indicator.'I'he indicator is next reset to .O49 on B, when the moment oi' inertiaI can be read under the hair line on A" and itis found to be 87.6 inf.

19. Find the diameter of a line shaft to transmit 600 horsepower at 400revolutions per minntei given Solution: Set 400 on "B (left section) to600 on A (left section) and align indicator with 448 on B (left section)when the diameter D=5.09 can be read under the hair line on Q2.

With the indicator set to any given number N on scales RI, R2, or R3,the following powers and roots can be read from the front working face,Figs. 1 and 5 of my improved slide rule: on A" read N, on K read N9, onCI read l/N-i, on D read N3 and on QI or Q2 read NM. It will be notedthat expressions such as N, N', and l/NJ cannot be obtained by directreading on existing slide rules.

The following examples will illustrate the ef- Use scale QI.

e scale Q2.

fectiveness of these scales in the solution of certain engineeringequations.

20. The minimum diameter of a Steamship shaft S=[(C.P.D2)/3f]1/". Given0:12, P=115, D=l8 and f=740, find S. Solution:

hence set indicator to 18 on QI and bring left index of C" to indicator.Place indicator over 12 on "C and bring left index of C to indicator,then move indicator to 115 on C, next bring 3 on C to indicator and as anal operation, move the indicator to 740 on CI, when the requireddiameter 5.86 inches can be read on R3.

21. Span between bearings of a shaft is calculated from the equationS=(CD2)1/I where S--the span in feet, C=a constant=2l6 and D=thediameter in inches. Given D=21/2 inches, nd S. S=[216(2.5)2]1/3=11.05ft. Solution: set indicator to 2.5 on QI, then bring 216 on CI inalignment with indicator. Next, move indicator to left index of CI whenthe required span S=ll.05 feet can be read on RI.

Find a: if a=25, b=375 and c=4.'15. x=(253 3751/2 4.751/3) 1/2, henceset indicator to 25 on R2 and bring left index of B to indicator. Placeindicator over 375 on B (left section) and set left index of K toindicator. Next, move indicator to 4.75 on K (left section) and read theresult 3::'113 on scale Q2.

in Fig. 2, reference is now made to the markings adjacent, and directlyto the' right of scales Qi and Q2'. The notation added here is a key tothe characteristic, or decimal point location, when using scales QI andQ2' in conjunction with scales QI and Q2. D, CI, and C. If `thediameters are given in mils or thousandths ci an inch, in accordancewith the Brown and Sharpe system of wire gauges, reference to a table ofthese gauges shows clearly that sizes from No. 0000 to 10 inclusive havethree digits, or a characteristic of 3; whereas, sizes from No. 11 to 30inclusive have two digits or a characteristic 2, and sizes from No. 31to 40 one digit with a characteristic of l. To the left of scale C onslide I (Fig. 1) is the scale for resistance, marked C., that normallycovers a temperature range from C. to 50 C. For the calculation ofresistances, any desired temperature within -this range is set to areference line marked R (resistance) situated immediately beneath the C.scale, and on the fixed bar J. Directly beneath, and in line with the Rreferred to above is the symbol which enables one to determine theresistance characteristic, definitely as follows: Wire diameters read onQI or Q2 have a characteristic as given at the extreme right of QI andQ2', (Fig. 2); corresponding squares or circular mils then being read onD, following rules for the characteristic already given. Finally, fromthe constant 5 or 6, depending on whether or not the slide has to bereset to the left, in order to obtain a reading on the CI scale, thecharacteristic representing circular mils is deducted, to give theresistance characteristic. The following example will make all thesepoints clear.

Examples illustrating resistance calculations set 20 C. to line R andmove hair-line Z over 16 on the Q2' scale. The diameter 50.8 mils cannow be read on Q2, since this size falls in the range 11-30, for whichthe characteristic is +2. Reading under the hair-line on D, the diametersquared or circular mils is found to be 2580 since sND=2N or 2 2=4. Theresistance per 1000' is read on CI under the hair-line, and because thereading is obtained without resetting the slide to the left, N1=54=1;hence the required resistance is approximately 4.0 ohms per 1000.

24. Find resistance per 1000 at 25 C.-wire size 250,000 circular mils.Solution: set 25 C. to line R and set indicator over 250,000 on D,reading the required resistance of .042 ohm on CI". Note that in thisexample Nr=56=1.

25. Find resistance per 1000 of a copper wire .250 in. diameter at 0 C.and 50 C. Solution: set 0 C. to R and indicator to 250 on QI, readingthe resistance R=0.153 ohm per 1000' on CI. Next move slide so that 50C. is in alignment with R when the resistance R=0.185 ohm per 1000 canbe read on CI.

26. Find resistance per 1000 of a No. wire at 50 C. Solution: set line Zto 10 on QI' and 50 C. to R. In this position no reading can be obtainedon the 01" scale, so place indicator over left index of CI, then bringright index of "01 to indicator, after which the indicator is reset tol0 on Qi' and a reading of 1.12 ohms per 1000 is obtained on C1. Notethat in this example Nr=65=l as given.

Considering the trigonometric scales of Fig. 3, and more particularlythe special markings to the extreme right thereof, as appearing moreclearly in the enlarged view Fig. 7; itis now evident that the 0" and +1in line with the tangent scales TI and T2 respectively, represents thecharacteristic for these scales, in accordance with the methods ofcalculation previously given. Likewise, the 1 and 0 in line with sinescales Si and S2 respectively represents their characteristic. The useof these trigonometric scales in conjunction with the new face scales ofFig. 1, QI and Q2, as well as RI, R2 and R3, is best shown by thefollowing examples:-

27. Let A2 sin b) 1/3. Find the value of a: when A=7.60 and b=35 30 or33=[('7.602 sin 30 30'31/3.

Solution: set indicator to '7.60 on Q2 (Fig. 1) and bring right index ofslide to indicator. Reset indicator to 35 30' on S2 (Fig. 3) and readthe required value of on R2 (Fig. 1) where it is found to be 3.225. Forthe characteristic, note that (7.60)2=2 1=2 and the product of (7.60)2sin 35 30 is 2+0=2, also the cube root of (7.60)2

sin 35 30 is (2+1)/3=1 as given, indicating that the result should beread on R2.

28. Let :c=(a3 sin b cos 6)-1/2. Find a: if a=1955, b==50 and c=87 30.Solution: set indicator to 1955v on RI (Fig. 1) and bring right index ofslide to indicator. Reset indicator to 50 on S2 (Fig. 3) andmove rightindex of slide to indicator. Next, move indicator to 87 30' on CSI andread a:=15,800 on QI (Fig. l). Characteristics are: (3X4) 2:10,10+0-1=9, and for the square root (9+1)/2=5 read on the QI scale.

29. Let x=(a tan b)1/2. Find :c if a=6 and b=78. Solution: set indicatorto 78 on T2 (Fig. 3) and bring right index of slide to indicator, thenreset indicator to 6 on C reading the result on Q2 where :r is found tobe '5.313.

Characteristics are: 1+1=2 and 2/2=1 as given,

the result being read on scale Q2.v

30. In a right triangle c=(a+b) 1f. Find c if a=3 and b=4. Solution:

Set indicator to .75 on D (Fig. 3) and read A=36 52' on TI. Bytrigonometry c=a/sln A, hence set indicator to 3 on "D and bring 36 52on S2 to indicator when the value of C=3/sln 36 52=5 can be read on Dunder the right index of C.

31. Find the secant of 30 on the D scale. By trigonometry sec a=l/cos a;hence, set indicator to left index of D" and bring 80 30' on CS2 toindicator. On "D opposite the right index oi.' C read'sec 80 30=6.08.

32. Find the cosecaiit of 25 30 on the D" scale. By trigonometry coseca=l/sin a; hence, set indicator to left index of Dl and bring 25 30 onS2 to indicator. On D opposite the right index of "C read cosec 2530'=2.32.

33. Find the value of (350 sec 89 1001/. Solution: set indicator to leftindex of D and bring 89 10' on CSI to indicator. Reset indicator to 350on "C when (350 sec 89 10)1/1='155 can oe read on QI.

Placing the sine and cosine scales on the slide permits the reading ofall trigonometric functions on the standard "D scale as shown by theexamples, and this is obviously a very decided advantage for extended orlengthy calculations.

I claim:

1. In a slide rule, a standard logarithme scale, an inverted logarithmicscale, a temperature scale and a reference line, the invertedlogarithmic scale and temperature scale bearing a fixed relationship toeach other and being movable relative to the standard scale andreference line, so arranged with respect to each other that wire sizesof a given material in circular mils on the standard logarithmic scaleare in alignment with their respective resistances in ohms per 1000 feeton the inverted logarithmic scale for any given position of thetemperature scale, so that the resistance of said wire per 1000 feet,for any circular mil area, and for any temperature can be read directlyon the inverted logarithmic scale.

2. In a slide rule, having a fixed bar and a sliding bar, a standardlogarithmic scale and reference line on the said ilxed bar, atemperature scale and an inverted logarithmic scale that bear a fixedrelationship to each other on the said sliding bar, so arranged withrespect to each other that wire sizes of a given material in circularmils on the standard logarithmic scale are in alignment with theirrespective resistances in ohms per 1000 feet on the inverted logarithmic.scale for any given position of the temperature scale, so that theresistance of said wire per 1000 feet, for any circular mil area, andfor-any temperature can be read directly on the inverted logarithmicscale.

3. In a slide rule, a twofold logarithmic scale, a standard logarithmicscale, an inverted logarithmic scale, a temperature scale and referenceline, the inverted scale and temperature scale bearing a fixedrelationship to each other and being movable relative to the twofoldlogarithmic scale, the standard logarithmic scale and the referenceline, so arranged with respect to each other that the diameters of awire of a given material in mils on the twofold logarithmic scale are inalignment with their respective resistances in ohms per 1000 feet on theinverted logarithmic scale for any given position of the temperaturescale, so that the resistance of said wire per 1000 feet for any givendiameter and for any temperature can be read directly onthe invertedlogarithmic scale.

4. In a slide rule, having a fixed bar and a sliding bar, a twofoldlogarithmic scale, a standard logarithmic scale, and reference line onthe said fixed bar, a temperature scale for the given material and aninverted logarithmic scale that bear a fixed relationship to each otheron the Said sliding bar, so arranged with respect to each other that thediameters of wire of said given material in mils on the twofoldlogarithmic scale are in alignment with their respective resistances inohms per 1000 feet on the inverted logarithmic scale for any givenposition of the temperature scale, so that the resistance of said wireper 1000 feet, for any given diameter and for any temperature can beread directly on the inverted logarithmic scale.

5. In a slide rule, a twofold scale of wire gauge.sizes, a twofoldlogarithmic scale, a standard logarithmic scale, an inverted logarithmicscale, a temperature scale for a given material and a reference line,the inverted scale and temperature scale bearing a fixed relationship toeach other and being 'movable relative tothe twofold scale of wire gaugesizes, the twofold logarithmic scale, the standard logarithmic scale andthe reference line, so arranged with respect to each other that the wiregauge sizes are in alignment with their respective resistances in ohmsper 1000 feet onthe inverted logarithmic scale, for any given positionof the temperature scale, so that the resistance of wire of said givenmaterial per 1000 feet, for any given gauge number and for anytemperature, can be read directly on the inverted logarithmic scale.

6. In a slide rule, having a fixed bar and a sliding bar, a twofoldscale of wire gauge sizes, a twofold logarithmic scale, a standardlogarithmic scale and reference line on the said xed bar, a temperaturescale for a given material, and an inverted logarithmic scale that beara fixed relationship to each other on the said sliding bar, so arrangedwith respect to each other that the wire gauge sizes are in alignmentwith their respective resistances in ohms per 1000 feet on the invertedlogarithmic scale, for any given position of the temperature scale, sothat the resistance of wire, of said given material per 1000 feet, forany given gauge number and for any temperature can be read directly onthe inverted scale.

ROY B. POOLE.

